CN112949057B - Equipment residual life prediction method integrating failure life data - Google Patents
Equipment residual life prediction method integrating failure life data Download PDFInfo
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- 238000006731 degradation reaction Methods 0.000 claims abstract description 101
- 230000015556 catabolic process Effects 0.000 claims abstract description 74
- 238000005259 measurement Methods 0.000 claims abstract description 16
- 238000009826 distribution Methods 0.000 claims description 32
- 238000012544 monitoring process Methods 0.000 claims description 9
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- BULVZWIRKLYCBC-UHFFFAOYSA-N phorate Chemical compound CCOP(=S)(OCC)SCSCC BULVZWIRKLYCBC-UHFFFAOYSA-N 0.000 claims 1
- 238000012423 maintenance Methods 0.000 abstract description 7
- 230000004927 fusion Effects 0.000 description 6
- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical compound [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 description 5
- 238000013398 bayesian method Methods 0.000 description 5
- 229910052744 lithium Inorganic materials 0.000 description 5
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- 230000003449 preventive effect Effects 0.000 description 1
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Abstract
The invention belongs to the technical field of reliability engineering, and relates to a residual life prediction method for fusing failure life data. The method comprises the following steps: step 1: establishing a device performance degradation model under the condition of imperfect prior information; step 2: estimating offline parameters; step 3: updating parameters online; step 4: the remaining life is predicted. The invention provides a residual life prediction method for fusing failure life data, and simultaneously considers the influence of variability and measurement errors among units, so that the method not only can be used for predicting and analyzing individual life and overall reliability life characteristic quantities of equipment, but also can be used as an effective analysis tool for predicting the residual life of the equipment, and provides powerful theoretical basis and technical support for maintenance and guarantee of the equipment based on states, thereby saving expenditure, avoiding unnecessary economic loss and having good engineering application value.
Description
Technical Field
The invention belongs to the technical field of reliability engineering, and particularly relates to a device residual life prediction method fusing failure life data.
Background
In practical engineering application, the prior information is often inaccurate and even lacks in the random degradation process of the system, namely, the prior information is imperfect. When imperfect prior information occurs, the residual life prediction accuracy also decreases. In order to overcome the influence of imperfect priori information on the residual life prediction, improve the residual life prediction precision, and research the relation between life data and degradation parameters aiming at the condition that priori degradation information does not exist, the residual life prediction method fused with failure life data is provided.
Disclosure of Invention
The purpose of the invention is that: the method and the device have the advantages that the influence of imperfect prior information is overcome by fully utilizing the equipment failure life data and the site degradation information, the individual life and the overall life characteristic quantity of the reliable equipment are scientifically predicted, and the problem of residual life prediction of the equipment under the condition of imperfect prior information is solved.
The technical scheme adopted by the invention is as follows:
a method for predicting the residual life of equipment by fusing failure life data comprises the following steps:
step 1: establishing a performance degradation model of the equipment under the condition of imperfect prior information;
step 2: off-line estimating a priori parameters of the model;
step 3: updating parameters online;
step 4: predicting the remaining life of the device.
Preferably, in the step 1, the prior information required in the remaining lifetime prediction method based on bayesian theory is: fixed parameters representing model commonality characteristics and prior information representing random parameters of sample individual differences in the degradation model; the performance degradation model of the equipment is built aiming at the linear and nonlinear random coefficient regression models respectively, and when the potential performance degradation process exceeds a failure threshold omega, the equipment is considered to be failed;
(1) Linear random coefficient regression model
The linear stochastic coefficient regression model is expressed as follows:
X(t)＝x 0 +λt (1)
wherein ,x0 Is in an initial state; lambda is a drift coefficient, characterizes the degradation speed, and makes x 0 =0; to represent individual differences between different devices, the drift coefficient lambda is regarded as a random variable, subject to normal distribution
The degradation process of the device can be expressed as follows, taking into account the measurement error existing between the observed degradation value Y (t) and the true degradation value X (t)
Y(t)＝X(t)+ε (2)
wherein ,representing a measurement error; generally epsilon is considered to be independent of each other and independent of lambda, the unknown parameters of which are +.>
(2) Nonlinear random coefficient regression model
The nonlinear stochastic coefficient regression model may be expressed as follows:
X(t)＝x 0 +λΛ(t；θ) (3)
wherein ,x0 Is an initial degradation value; lambda is a drift coefficient and represents degradation speed; Λ (t; θ) is a continuous nonlinear function with respect to time t, characterizing the nonlinearity of the device degradation process, where θ is a fixed coefficient describing the nonlinear relationship of the device degradation state with time; without losing generality, let x 0 =0, Λ (t; θ) =tθ; to represent individual differences between different devices, the drift coefficient lambda is regarded as a random variable, subject to normal distribution
The monitored degradation process of the device can be expressed as follows, taking into account the measurement error existing between the observed degradation value Y (t) and the true degradation value X (t)
Y(t)＝X(t)+ε (4)
wherein ,representing a measurement error; generally considered as epsilon independent and independent of lambda, unknown parameters of the model for the nonlinear wiener process +.>
The service life of the equipment based on the random coefficient regression model is defined as the moment when the performance degradation state { X (T), T is more than or equal to 0} of the equipment reaches the failure threshold value, and if ω represents the failure threshold value of the equipment, the service life T of the equipment can be represented as follows
T＝{t:X(t)≥ω|x 0 ＜ω} (5)。
Preferably, in step 2, before estimating the prior parameters of the model, the fixed parameters of the model are estimated;
(1) Linear random coefficient regression model
First, fixed parameters of the model are estimated, the device at t k Time of day, y acquired 1 : k ＝[y 1 ,y 2 ,…,y k ]Is the time t of monitoring the device 1 ,t 2 ,...t k Is to observe degradation data in situ The log likelihood function of (2) may be expressed as follows:
maximizing the log-likelihood function (6)
Before estimating the a priori distribution of the drift coefficients, the following conclusion is given
According to the nature of the random coefficient regression model, the degradation process described by the formula (1) is satisfied, and the equipment failure time T of the degradation process is v Satisfy the following requirements
Then, the prior distribution of drift coefficients is solved by using maximized likelihood estimation
Assume that historical failure data T of M devices is obtained 1:M ＝{t 1 ,t 2 ,…,t m Then (V) isThe log likelihood function of (2) may be expressed as follows:
mu is determined for (9) λ ,Is derived from deflection of
Let formula (10) and formula (11) equal zero to obtain and />Estimation
(2) Nonlinear random coefficient regression model
First, fixed parameters of the model are estimated, assuming the device is at t k Time of day, y acquired 1:k ＝[y 1 ,y 2 ,…,y k ]Is the time t of monitoring the device 1 ,t 2 ,…,t k Is to observe degradation data in situ The log likelihood function of (2) may be expressed as follows:
maximizing formula (14) to obtainLimited estimation of (2)
Substituting equation (15) into equation (14) to obtain the contour likelihood function of θ
Maximizing the above formula to obtainAdopts Fminresearch function based on simplex method in MATLAB software to search maximum value, finally obtains ++>This estimate +.>Substituting formula (15) again to obtain final +.>
Then, the prior distribution of drift coefficients is solved by using maximized likelihood estimation
According to the property of the random coefficient regression model, the equipment failure time T v The probability density function of (2) is
Assume that historical failure data T of M devices is obtained 1:M ＝{t 1 ,t 2 ,…,t m Then (V) isThe log likelihood function of (2) may be expressed as follows:
mu is determined for (18) λ ,Is derived from deflection of
Let formula (19) and formula (20) equal zero to obtain and />Estimation
Preferably, in step 3, the random coefficient distribution is updated online by using the bayesian principle, and the specific process is as follows:
(1) Linear random coefficient regression model
Assume that the device is at t k Time of day, y acquired 1 : k ＝[y 1 ,y 2 ,…,y k ]Is the detection time t 1 ,t 2 ,…,t k Observed degradation data of a device to be estimated offline A priori information mu as drift parameter lambda λ0 ,/>I.e.According to Bayesian theory, observed degradation data y is detected 1 : k The random coefficients after that are also subject to normal distribution, namely:
wherein ：
(2) Nonlinear random coefficient regression model
Assume that the device is at t k Time of day, y acquired 1 : k ＝[y 1 ,y 2 ,…,y k ]Is the detection time t 1 ,t 2 ,…,t k Observed degradation data of a device to be estimated offlineA priori information mu as drift parameter lambda λ0 ,/>I.e.According to Bayesian theory, observed degradation data y is detected 1:k Then, obtaining the random coefficient lambda posterior distribution of the nonlinear random coefficient regression model as
wherein ：
preferably, in step 4, the remaining life prediction process is as follows:
let l k Indicating that the device is at t k Remaining lifetime of the device at the moment, lifetime t=t of the device is obtained k +l k The degradation process represented by formula (1) can be converted into
Z(l k )＝X(l k +t k )-X(t k )＝λl k (27)
The device is at t k The remaining useful life at the moment in time can be expressed as the degradation process { Z (l k ),l k More than or equal to 0 and passing through failure threshold omega k ＝ω-x k The remaining life is defined as
Without loss of generality, Z (0) =0; consider at t k At a time when the rotating machine has not failed, the current degradation state should be less than the failure threshold, using a truncated normal distribution to describe ω -x k > 0, i.e
(1) The residual life probability density function of the linear random coefficient regression model is
The residual life probability density function of the linear random coefficient regression model is derived as follows:
wherein ,
μ＝ω-y k (30)
2) Nonlinear random coefficient regression model
The residual life probability density function of the nonlinear random coefficient regression model is derived as follows:
wherein ：
μ＝ω-y k (35)
based on the above process, for the imperfect prior information case, the residual life prediction of the device can be achieved by fusing the failure life data.
The invention has the beneficial effects that: the invention provides a residual life prediction method of complex equipment under the condition of imperfect prior information. The method can predict and analyze the individual life and the overall reliability life characteristic quantity of the equipment, and provide powerful theoretical basis and technical support for maintenance and guarantee based on the state of the equipment, thereby saving the expenditure, avoiding unnecessary economic loss and having good engineering application value.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is experimental degradation data for a lithium battery; (a) calendar time; (b) number of cycles;
FIG. 2 is a comparison of remaining life predictions of a fused failure life data method and a Bayesian method;
FIG. 3 is a Relative Error (RE) and Mean Square Error (MSE) of a fused dead life data method (M1) and a Bayesian method (M2) residual life prediction; (a) Relative Error (RE); (b) Mean Square Error (MSE).
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention.
Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The validity of the invention is verified based on lithium battery experimental degradation data disclosed by NASA. The data comprise drift coefficient data recorded by four lithium batteries at different state monitoring time points in the actual use process. In the experiment, according to the technical index of the lithium battery, the failure threshold value is selected as follows. The monitoring interval is one cycle, recorded as the number of cycles. Measurement data corresponding to the lithium battery degradation monitoring full life cycle is shown in fig. 1. Without loss of generality, we estimate a priori parameters using the life data of battery No.5 as experimental battery, and battery nos. 6, 7 and 18 as a priori information.
Based on this, a device remaining lifetime prediction method that fuses failure lifetime data, comprising the steps of:
step 1: establishing equipment performance degradation model under imperfect prior information condition
The prior information needed in the residual life prediction method based on the Bayesian theory is as follows: fixed parameters representing model commonalities and prior information representing random parameters of sample individual differences in the degradation model. In practical use, situations may sometimes occur in which the prior information is not accurate enough or even completely absent. For this reason, we propose a residual life prediction method that fuses the failure life data. Historical failure data of similar devices can be obtained from maintenance records of the similar devices, and field degradation data can be obtained directly on site by using monitoring devices. The performance degradation model of the equipment is firstly built aiming at the linear and nonlinear random coefficient regression models respectively, and the equipment is considered to be invalid when the potential performance degradation process exceeds a failure threshold omega.
(1) Linear random coefficient regression model
The regression model is a stochastic mathematical model originally proposed for degradation modeling, and is called a stochastic coefficient regression model when the regression coefficients in the model are random variables. The model mathematical expression is simple and can be widely applied to degradation modeling in various fields. The basic stochastic coefficient regression model is represented as follows:
X(t)＝x 0 +λt (1)
wherein ,x0 Is in an initial state; lambda is a drift coefficient, characterizes the degradation speed, and makes x 0 =0; to represent individual differences between different devices, the drift coefficient lambda is regarded as a random variable, subject to normal distribution
In the actual running process of the equipment, due to factors such as data acquisition by using a non-ideal measurement method, interference of a random environment and the like, the observed data cannot truly reflect the actual degradation level of the equipment. The degradation process of the device can be expressed as follows, taking into account the measurement error existing between the observed degradation value Y (t) and the true degradation value X (t)
Y(t)＝X(t)+ε (2)
wherein ,representing a measurement error; generally epsilon is considered to be independent of each other and independent of lambda, the unknown parameters of which are +.>
(2) Nonlinear random coefficient regression model
In real life, most equipment degradation processes do not exhibit perfect linear relationships, and nonlinear degradation processes are more prevalent. The nonlinear stochastic coefficient regression model may be expressed as follows:
X(t)＝x 0 +λΛ(t；θ) (3)
wherein ,x0 Is an initial degradation value; lambda is a drift coefficient and represents degradation speed; Λ (t; θ) is a continuous nonlinear function with respect to time t, characterizing the nonlinearity of the device degradation process, where θ is a fixed coefficient describing the nonlinear relationship of the device degradation state with time; without losing generality, let x 0 ＝0，Λ(t；θ)＝t θ The method comprises the steps of carrying out a first treatment on the surface of the To represent individual differences between different devices, the drift coefficient lambda is regarded as a random variable, subject to normal distribution
In the actual running process of the equipment, due to factors such as data acquisition by using a non-ideal measurement method, interference of a random environment and the like, the observed data cannot truly reflect the actual degradation level of the equipment. The monitored degradation process of the device can be expressed as follows, taking into account the measurement error existing between the observed degradation value Y (t) and the true degradation value X (t)
Y(t)＝X(t)+ε (4)
wherein ,representing a measurement error; generally considered as epsilon independent and independent of lambda, unknown parameters of the model for the nonlinear wiener process +.>
The service life of the equipment based on the random coefficient regression model is defined as the moment when the performance degradation state { X (T), T is more than or equal to 0} of the equipment reaches the failure threshold value, and if ω represents the failure threshold value of the equipment, the service life T of the equipment can be represented as follows
T＝{t:X(t)≥ω|x 0 ＜ω} (5)。
Step 2: off-line estimating model prior parameter
Before estimating the prior parameters of the model, estimating the fixed parameters of the model;
(1) Linear random coefficient regression model
First, fixed parameters of the model are estimated, the device at t k Time of day, y acquired 1 : k ＝[y 1 ,y 2 ,…,y k ]Is the time t of monitoring the device 1 ,t 2 ,...t k Is to observe degradation data in situ The log likelihood function of (2) may be expressed as follows:
maximizing the log-likelihood function (6)
Before estimating the a priori distribution of the drift coefficients, the following conclusion is given
According to the nature of the random coefficient regression model, the degradation process described by the formula (1) is satisfied, and the equipment failure time T of the degradation process is v Satisfy the following requirements
Then, the prior distribution of drift coefficients is solved by using maximized likelihood estimation
Assume that historical failure data T of M devices is obtained 1 : M ＝{t 1 ,t 2 ,…,t m Then (V) isThe log likelihood function of (2) may be expressed as follows:
mu is determined for (9) λ ,Is derived from deflection of
Let formula (10) and formula (11) equal zero to obtain and />Estimation
(2) Nonlinear random coefficient regression model
First, fixed parameters of the model are estimated, assuming the device is at t k Time of day, y acquired 1 : k ＝[y 1 ,y 2 ,…,y k ]Is the time t of monitoring the device 1 ,t 2 ,…,t k Is to observe degradation data in situ The log likelihood function of (2) may be expressed as follows:
maximizing formula (14) to obtainLimited estimation of (2)
Substituting equation (15) into equation (14) to obtain the contour likelihood function of θ
Maximizing the above formula to obtainAdopts Fminresearch function based on simplex method in MATLAB software to search maximum value, finally obtains ++>This estimate +.>Substituting formula (15) again to obtain final +.>
Then, the prior distribution of drift coefficients is solved by using maximized likelihood estimation
According to the property of the random coefficient regression model, the equipment failure time T v The probability density function of (2) is
Assume that historical failure data T of M devices is obtained 1:M ＝{t 1 ,t 2 ,…,t m Then (V) isThe log likelihood function of (2) may be expressed as follows:
mu is determined for (18) λ ,Is derived from deflection of
Let formula (19) and formula (20) equal zero to obtain and />Estimation
Step 3: on-line updating parameters
(1) Linear random coefficient regression model
On-line updating of random coefficient distribution by Bayes principle, assuming that the device is at t k Time of day, y acquired 1:k ＝[y 1 ,y 2 ,…,y k ]Is the detection time t 1 ,t 2 ,…,t k Observed degradation data of a device to be estimated offline A priori information mu as drift parameter lambda λ0 ,/>I.e. < ->According to Bayesian theory, observed degradation data y is detected 1:k The random coefficients after that are also subject to normal distribution, namely:
wherein ：
(2) Nonlinear random coefficient regression model
On-line updating of random coefficient distribution by Bayes principle, assuming that the device is at t k Time of day, y acquired 1:k ＝[y 1 ,y 2 ,…,y k ]Is the detection time t 1 ,t 2 ,…,t k Observed degradation data of a device to be estimated offline A priori information mu as drift parameter lambda λ0 ,/>I.e. < ->According to Bayesian theory, observed degradation data y is detected 1:k Then, obtaining the random coefficient lambda posterior distribution of the nonlinear random coefficient regression model as
wherein ：
step 4: predicting remaining life
Let l k Indicating that the device is at t k Remaining lifetime of the device at the moment, lifetime t=t of the device is obtained k +l k The degradation process represented by formula (1) can be converted into
Z(l k )＝X(l k +t k )-X(t k )＝λl k (27)
The device is at t k The remaining useful life at the moment in time can be expressed as the degradation process { Z (l k ),l k More than or equal to 0 and passing through failure threshold omega k ＝ω-x k The remaining life is defined as
Without loss of generality, Z (0) =0; consider at t k At a time when the rotating machine has not failed, the current degradation state should be less than the failure threshold, using a truncated normal distribution to describe ω -x k > 0, i.e
(1) The residual life probability density function of the linear random coefficient regression model is
The residual life probability density function of the linear random coefficient regression model is derived as follows:
wherein ,
μ＝ω-y k (30)
2) Nonlinear random coefficient regression model
The residual life probability density function of the nonlinear random coefficient regression model is derived as follows:
wherein ：
μ＝ω-y k (35)
taking a nonlinear random coefficient regression model as an example, taking a No.5 battery as an evaluated object, and using degradation data of other batteries to calculate priori information of residual life prediction to obtain correct priori information for residual life prediction as mu λ ＝4.1×10 -3 ，b= 1.1539. Normalization is performed when calculating the parameter estimation results, i.e. the degradation data is subtracted from the initial values. Furthermore, the failure times of the No.6, no.7, no.18 batteries were 69.5, 110.3 and 51, respectively, which could be used as a priori failure data for the fusion failure life data prediction method. The remaining life distributions of the fusion failure life data prediction method and the bayesian method are calculated respectively, and the results are shown in fig. 2. It can be seen that the remaining life distribution calculated by both methods can cover the actual remaining life. However, the residual life distribution of the fusion failure life data prediction method is more concentrated near the actual residual life, and the residual life distribution is narrower, which means that the fusion failure life data prediction method has higher residual life prediction accuracy.
Leaf of BettyThe reason why the prediction accuracy of the si method is degraded is due to imperfect prior information. As can be seen from fig. 1, the degradation data of the No.6 and No.18 batteries have significant linear degradation characteristics, which is also the cause of the estimated value of the nonlinear coefficient b being 1.1539. In addition, as can be seen from FIG. 1, the measurement error uncertainty of the No.5 battery data is significantly smaller than that of the No.6, no.7 and No.18 battery data, thereby causing excessive amounts of measurement error uncertaintyFurthermore, as can be seen from fig. 2, the remaining life predicted by the bayesian method is larger than the actual remaining life, so that preventive maintenance time can be delayed, effective maintenance cannot be performed before equipment fails, the remaining life predicted by the fused failure life data method is close to the actual remaining life, and according to engineering practice, the cost of performing maintenance after the equipment fails is larger than the cost of performing maintenance in advance under the same condition, so that the superiority of the fused failure life data prediction method provided by the invention is verified.
To further compare the residual life prediction effects of the two algorithms, the relative error and mean square error of the residual life predictions of the two methods are calculated, as shown in fig. 3.
The mean square error of the fusion failure life data prediction method is obviously smaller than that of a Bayesian method, so that the fusion failure life data prediction method can overcome the influence of incomplete prior information, and the prediction result is more in line with the degradation characteristics of the equipment to be evaluated, so that the prediction accuracy of the residual life is higher. In summary, the method provided by the invention can improve the accuracy of the residual life estimation, can effectively overcome the influence of imperfect prior information, reduces the relative error of the residual life estimation, and further verifies the validity of the method.
The foregoing is merely illustrative of the present invention and not restrictive, and other modifications and equivalents thereof may occur to those skilled in the art without departing from the spirit and scope of the present invention.
Claims (1)
1. The method for predicting the residual life of the equipment by fusing the failure life data is characterized by comprising the following steps of:
step 1: establishing a performance degradation model of the equipment under the condition of imperfect prior information;
step 2: off-line estimating a priori parameters of the model;
step 3: updating parameters online;
step 4: predicting the residual life of equipment;
in the above step 1, the prior information required in the remaining lifetime prediction method based on bayesian theory is: fixed parameters representing model commonality characteristics and prior information representing random parameters of sample individual differences in the degradation model; the performance degradation model of the equipment is built aiming at the linear and nonlinear random coefficient regression models respectively, and when the potential performance degradation process exceeds a failure threshold omega, the equipment is considered to be failed;
(1) Linear random coefficient regression model
The linear stochastic coefficient regression model is expressed as follows:
X(t)＝x 0 +λt(1)
wherein ,x0 Is in an initial state; lambda is a drift coefficient, characterizes the degradation speed, and makes x 0 =0; to represent individual differences between different devices, the drift coefficient lambda is regarded as a random variable, subject to normal distribution
The degradation process of the device can be expressed as follows, taking into account the measurement error existing between the observed degradation value Y (t) and the true degradation value X (t)
Y(t)＝X(t)+ε (2)
wherein ,representing a measurement error; generally epsilon is considered to be independently co-distributed and is related to lambdaIndependently, for the basic linear random coefficient regression model, its unknown parameters +.>
(2) Nonlinear random coefficient regression model
The nonlinear stochastic coefficient regression model may be expressed as follows:
X(t)＝x 0 +λΛ(t；θ) (3)
wherein ,x0 Is an initial degradation value; lambda is a drift coefficient and represents degradation speed; Λ (t; θ) is a continuous nonlinear function with respect to time t, characterizing the nonlinearity of the device degradation process, where θ is a fixed coefficient describing the nonlinear relationship of the device degradation state with time; without losing generality, let x 0 ＝0，Λ(t；θ)＝t θ The method comprises the steps of carrying out a first treatment on the surface of the To represent individual differences between different devices, the drift coefficient lambda is regarded as a random variable, subject to normal distribution
The monitored degradation process of the device can be expressed as follows, taking into account the measurement error existing between the observed degradation value Y (t) and the true degradation value X (t)
Y(t)＝X(t)+ε (4)
wherein ,representing a measurement error; generally considered as epsilon independent and independent of lambda, unknown parameters of the model for the nonlinear wiener process +.>
The service life of the equipment based on the random coefficient regression model is defined as the moment when the performance degradation state { X (T), T is more than or equal to 0} of the equipment reaches the failure threshold value, and if ω represents the failure threshold value of the equipment, the service life T of the equipment can be represented as follows
T＝{t:X(t)≥ω|x 0 ＜ω} (5)；
In step 2, before estimating the prior parameters of the model, estimating the fixed parameters of the model;
(1) Linear random coefficient regression model
First, fixed parameters of the model are estimated, the device at t k Time of day, y acquired 1:k ＝[y 1 ,y 2 ,…,y k ]Is the time t of monitoring the device 1 ,t 2 ,...t k Is to observe degradation data in situ The log likelihood function of (2) may be expressed as follows:
maximizing the log-likelihood function (6)
Before estimating the a priori distribution of the drift coefficients, the following conclusions are drawn:
according to the nature of the random coefficient regression model, the degradation process described by the formula (1) is satisfied, and the equipment failure time T of the degradation process is v Satisfy the following requirements
The prior distribution of drift coefficients is then solved using maximized likelihood estimation:
assume that historical failure data T of M devices is obtained 1:M ＝{t 1 ,t 2 ,…,t m Then (V) isThe log likelihood function of (2) may be expressed as follows:
concerning (9)Is derived from deflection of
Let formula (10) and formula (11) equal zero to obtain and />Estimation
(2) Nonlinear random coefficient regression model
First, fixed parameters of the model are estimated, assuming the device is at t k Time of day, y acquired 1:k ＝[y 1 ,y 2 ,…,y k ]Is the device monitoring timet 1 ,t 2 ,…,t k Is to observe degradation data in situ The log likelihood function of (2) may be expressed as follows:
maximizing formula (14) to obtainLimited estimation of (2)
Substituting equation (15) into equation (14) to obtain the contour likelihood function of θ
Maximizing the above formula to obtainAdopts Fminresearch function based on simplex method in MATLAB software to search maximum value, finally obtains ++>This estimate +.>Substituting formula (15) again to obtain final +.>
The prior distribution of drift coefficients is then solved using maximized likelihood estimation:
according to the property of the random coefficient regression model, the equipment failure time T v The probability density function of (2) is
Assume that historical failure data T of M devices is obtained 1:M ＝{t 1 ,t 2 ,…,t m Then (V) isThe log likelihood function of (2) may be expressed as follows:
concerning (18)Is derived from deflection of
Let formula (19) and formula (20) equal zero to obtain and />Estimation
In step 3, the random coefficient distribution is updated online by using the Bayesian principle, and the specific process is as follows:
(1) Linear random coefficient regression model
Assume that the device is at t k Time of day, y acquired 1:k ＝[y 1 ,y 2 ,…,y k ]Is the detection time t 1 ,t 2 ,…,t k Observed degradation data of a device to be estimated offlineA priori information as drift parameter lambda>I.e. < ->According to Bayesian theory, observed degradation data y is detected 1:k The random coefficients after that are also subject to normal distribution, namely:
wherein ：
(2) Nonlinear random coefficient regression model
Assume that the device is at t k Time of day, y acquired 1:k ＝[y 1 ,y 2 ,…,y k ]Is the detection time t 1 ,t 2 ,…,t k Observed degradation data of a device to be estimated offlineA priori information as drift parameter lambda>I.e. < ->According to Bayesian theory, observed degradation data y is detected 1:k Then, obtaining the random coefficient lambda posterior distribution of the nonlinear random coefficient regression model as
wherein ：
in step 4, the remaining life prediction process is as follows:
let l k Indicating that the device is at t k Remaining lifetime of the device at the moment, lifetime t=t of the device is obtained k +l k The degradation process represented by formula (1) can be converted into
Z(l k )＝X(l k +t k )-X(t k )＝λl k (27)
The device is at t k The remaining useful life at the moment in time can be expressed as the degradation process { Z (l k ),l k More than or equal to 0 and passing through failure threshold omega k ＝ω-x k The remaining life is defined as
Without loss of generality, Z (0) =0; consider at t k At a time when the rotating machine has not failed, the current degradation state should be less than the failure threshold, using a truncated normal distribution to describe ω -x k > 0, i.e
(1) The residual life probability density function of the linear random coefficient regression model is derived from the residual life probability density function of the linear random coefficient regression model as follows:
wherein ,
μ＝ω-y k (30)
(2) Nonlinear random coefficient regression model
The residual life probability density function of the nonlinear random coefficient regression model is derived as follows:
wherein ：
μ＝ω-y k (35)
based on the above process, for the imperfect prior information case, the residual life prediction of the device can be achieved by fusing the failure life data.
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Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103488881A (en) * | 2013-09-06 | 2014-01-01 | 中国人民解放军第二炮兵工程大学 | Equipment residual service life prediction method under the condition of uncertain degradation measured data |
| GB201420843D0 (en) * | 2014-11-24 | 2015-01-07 | Thunot Andre And Robertson Paul | Cell internal impedance diagnostic system |
| CN106484949A (en) * | 2016-09-12 | 2017-03-08 | 西安理工大学 | Momenttum wheel fail-safe analysis and method for predicting residual useful life based on degraded data |
| CN107194478A (en) * | 2017-06-21 | 2017-09-22 | 中国人民解放军国防科学技术大学 | Merge the unit method for predicting residual useful life of lifetime data and Performance Degradation Data |
| CN109829137A (en) * | 2019-01-22 | 2019-05-31 | 中国人民解放军火箭军工程大学 | The life-span prediction method and system of non-linear degradation equipment under a kind of cyclic stress |
| CN111258297A (en) * | 2020-01-17 | 2020-06-09 | 北京大学 | Equipment health index construction and service life prediction method based on data fusion network |
| CN111460692A (en) * | 2020-04-26 | 2020-07-28 | 中国人民解放军火箭军工程大学 | Equipment residual life prediction method and system considering degradation rate mutual influence |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108959676B (en) * | 2017-12-22 | 2019-09-20 | 北京航空航天大学 | It is a kind of to consider the degeneration modeling effectively impacted and life-span prediction method |
-
2021
- 2021-02-26 CN CN202110222526.4A patent/CN112949057B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103488881A (en) * | 2013-09-06 | 2014-01-01 | 中国人民解放军第二炮兵工程大学 | Equipment residual service life prediction method under the condition of uncertain degradation measured data |
| GB201420843D0 (en) * | 2014-11-24 | 2015-01-07 | Thunot Andre And Robertson Paul | Cell internal impedance diagnostic system |
| CN106484949A (en) * | 2016-09-12 | 2017-03-08 | 西安理工大学 | Momenttum wheel fail-safe analysis and method for predicting residual useful life based on degraded data |
| CN107194478A (en) * | 2017-06-21 | 2017-09-22 | 中国人民解放军国防科学技术大学 | Merge the unit method for predicting residual useful life of lifetime data and Performance Degradation Data |
| CN109829137A (en) * | 2019-01-22 | 2019-05-31 | 中国人民解放军火箭军工程大学 | The life-span prediction method and system of non-linear degradation equipment under a kind of cyclic stress |
| CN111258297A (en) * | 2020-01-17 | 2020-06-09 | 北京大学 | Equipment health index construction and service life prediction method based on data fusion network |
| CN111460692A (en) * | 2020-04-26 | 2020-07-28 | 中国人民解放军火箭军工程大学 | Equipment residual life prediction method and system considering degradation rate mutual influence |
Non-Patent Citations (3)
| Title |
|---|
| 《Remaining Useful Lifetime Prediction for the Equipment with the Random Failure Threshold》;Zezhou Wang等;《2019 Prognostics and System Health Management Conference(PHM-Qingdao)》;20191231;全文 * |
| 《基于不完美先验信息的随机系数回归模型剩余寿命预测方法》;万昌豪等;《北京航空航天大学学报》;20201012;第1-13页 * |
| 不确定退化测量数据下的剩余寿命估计;司小胜等;《电子学报》;20150115(第01期);全文 * |
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